Bibliographic record
Abstract
Abstract: Accuracy of the quarter-point and transition elements is investigatedon one- and two-dimensional problems with inverse square-root singularity. It isdemonstrated that most coefficients of the stiffness matrix of the quarter-point el-ement are unbounded. However, numerical integration produces finite values ofthese coefficients. Influence of several parameters on the error in determining thestress intensity factor is studied. Solution accuracy can be improved using specialdistribution of element sizes and increasing the element integration order in theradial direction.Keywords: Finite element method, linear fracture mechanics, quarter-point ele-ment.1 IntroductionThe quarter-point singular element has been employed in finite element modelingof crack-tip fields for several decades. It was proposed by Henshell and Shaw(1975) and Barsoum (1976, 1977). They showed that by shifting midside nodes ofa quadratic isoparametric element to quarter-side positions it is possible to modelexactly square-root singularity of the strains and stresses near the crack tip. Hib-bitt (1977) and Ying (1982) demonstrated that the strain energy of a quarter-pointelement degenerated into a triangle is always bounded. Lynn and Ingraffea (1978)generalized the quarter-point element to the so-called transition element. Tran-sition elements are located in the finite element mesh at some distance from thecrack tip and exactly represent the square-root singularity with the pole at the cracktip. Midside nodes of transition elements are placed at positions between quarter-and mid-point. The placement of midside nodes depends on the distance of thetransition element from the crack tip.While this study considers the use of quarter-point elements with the finite ele-
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".